Question

-7x+2y<2 and 3x+4y>=-12

Answer 1

Answer:

Here's what I get  

Step-by-step explanation:

Your inequalities are

(1) -7x + 2y< 2

(2) 3x + 4y ≥   -12

1. Solve each inequality for y

(a) From (1)

$\begin{array}{rcl}-7x + 2y & < & 2\\2y&< & 7x + 2\\y& < & \frac{7}{2} x + 1\\\end{array}$

(b) From (2)

$\begin{array}{rcl}3x + 4y & \geq & -12\\4y & \geq &-3x -12\\y& \geq & -\frac{3}{4}x -3\\\end{array}$

2. Make a table with a few points for each graph

$\begin{array}{rrr}\mathbf{x} & \mathbf{y_{(1)}}& \mathbf{y_{(2)}}\\-4 && 0\\-2 & -6 & \\0 & 1 & -3\\2 &8 & \\4 & & -6\\\end{array}$

3. Plot the graphs of the equalities

We get the graphs in Fig.1.

4. Check one or two points to find those in the solution set.

Check the point (0,0).

For Equation (1),  

0 < 2. TRUE. (0,0) is in the solution set.

Shade the region to the right of the blue line blue (Fig. 2). Make the line dashed, because points on the line do not satisfy the inequality.

For Equation (2),

0 ≥ -12. TRUE. (0,0) is in the solution set.

Shade the region to the right of the orange solid line and including the line, orange (Fig. 3).

5. Identify a point in the solution set

The solution set for the system of inequalities is the area in which the blue and orange fields overlap

One point in the solution set is the origin, (0, 0)